Question

In a Young's double slit experiment, ${\text{I}}_0$ is the maximum intensity and $\beta$ is the fringe width. Intensity at point $\text{P}$ which is distance $\text{x}$ from central maxima is

• A. $I_{0}cos\frac{\pi x}{\beta }$
• B. $4I_{0}co{s}^2\frac{\pi x}{\beta }$
• C. $I_{0}co{s}^2\frac{\pi x}{\beta }$
• D. $\frac{I_0}{4}co{s}^2\frac{\pi x}{\beta }$

Answer 1

Answer: (C)

Path difference at point $P=\frac{xd}{D}$
$\therefore$ Phase difference at $P=\frac{2\pi }{\lambda }\frac{xd}{D}=\frac{2\pi x}{\beta }$
$\therefore$ Intensity at $P=I+I+2Icos\frac{2\pi x}{\beta }$
$=2I\left[1+cos\frac{2\pi x}{\beta }\right]\left[\because I_0=4I\right]$
$=4Ico{s}^2\frac{\pi x}{\beta }=I_{0}co{s}^2\frac{\pi x}{\beta }$